Fresh watermelon contains 90% water by weight whereas dry watermelon contains 20% water by weight. Ben buys 64 kg of fresh watermelon for $160. At what price should Ben sell the dry watermelon to get a profit of 20%?
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Wait, this is 705-805 level? I thought it was just a straightforward percentage problem until I read the choices. The 20% water in dry watermelon threw me off.
Right? The trick is realizing the non-water part stays constant. That's the whole game.
The key here is that the solid content (non-water) doesn't change when it dries. So from 64 kg fresh, solids = 10% = 6.4 kg. In dry watermelon, solids are 80%, so total dry weight = 6.4 / 0.8 = 8 kg. Then 20% profit on $160 is $192, so price per kg = 24. Answer A.
Thanks, that constant-solid insight is exactly what I missed. I was trying to do it with water percentages directly and got lost.
Clean explanation. I did the same but kept second-guessing because 24 seemed too low for 8 kg.
I got 30 and I don't see where I went wrong. I did 64 * 0.1 = 6.4, then 6.4 / 0.2? That gave 32 total dry weight, then 192/32 = 6. Clearly wrong. Can someone break down why we divide by 0.8 and not 0.2?
Because 20% is the water part, so solids are 80%. You want the total weight whose 80% is 6.4. So 6.4/0.8.
Hard question but fair. Took me way too long to realize I should track the non-water component. Definitely a 705+ for the trap alone.
Yeah, the wording makes it seem like a simple water loss problem, but it's really about conservation of mass.
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.